Generalized metallic means
Abstract
The metallic means (also known as metallic ratios) may be defined as the limiting ratio of consecutive terms of sequences connected to the Fibonacci sequence via the INVERT transform. For example, the Pell sequence (invert transform of the Fibonacci sequence) gives the socalled silver mean, and the invert transform of the Pell sequence leads to the bronze mean. The limiting ratio of the Fibonacci sequence itself is known as the golden mean or ratio. We introduce a new family of kthdegree metallic means obtained through invert transforms of the generalized kthorder Fibonacci sequence. As it is the case for k=2, each generalized metallic mean is shown to be the unique positive root of a kthdegree polynomial determined by the sequence.
 Publication:

arXiv eprints
 Pub Date:
 January 2019
 arXiv:
 arXiv:1901.02619
 Bibcode:
 2019arXiv190102619G
 Keywords:

 Mathematics  Number Theory;
 11B39
 EPrint:
 6 pages. To appear in The Fibonnaci Quarterly